Fill a medium skillet halfway with salted water; bring to a boil. Add the asparagus and cook for 2 minutes. Drain in a colander; rinse with cold water. Toss with 2 teaspoons olive oil; season with salt and pepper.
Preheat a grill to medium. Cut six 12-inch pieces of kitchen string. In a small bowl, stir together the jam, lemon juice and remaining 1 teaspoon olive oil.
Pound each piece of chicken about 1/4 inch thick and season with salt and pepper; place skinned side down on a baking sheet. Divide the asparagus into 6 equal portions and place each portion crosswise in the center of a chicken cutlet. Roll up each cutlet and tie closed with the kitchen string. Brush the rollups with the jam mixture; season with salt and pepper.
Transfer the chicken rollups to the grill, cover and cook, turning occasionally, until browned, about 15 minutes.
Meanwhile, in a small saucepan, bring 1 1/4 cups water and 1/2 teaspoon salt to a boil. Stir in the couscous, carrots and mango, cover, turn off the heat and let stand for 5 minutes. Fluff with a fork and serve with the chicken.